AI 中文总结
本研究提出归一化带符号原积分用于任意时间求解器评估，对比相关核函数，在路由与模型保真度任务上验证其可保留面板排序，相关资源已公开。
AI 中文摘要
任意时间求解器在终止前会返回可用解，并在剩余时间内对解进行优化，其进展通常由原积分、最终间隙或收敛曲线总结。每种总结方式都留下了重要选择空间：如何在首次得到可行解前对运行过程打分，是否截断劣质当前解，以及参考值是在实验后更新还是预先固定。当运行未产生有效当前解或改进了已公布的最佳已知值时，这些选择会凸显出来。我们研究一种由有界相对间隙构建的归一化带符号原积分，它为空运行分配内在最差值，无需接受阈值，且为优于固定参考的当前解分配负瞬时间隙。我们将平滑差和核与Berthold最大归一化间隙的带符号版本进行比较，并将前者作为默认方案。我们还区分分析时参考策略与预先固定参考策略，建议结合原始最终间隙、平均收敛曲线和目标达成曲线来解读分数。我们在五臂路由案例和两个模型保真度梯级上评估这些选择。本研究中，两种带符号核保留了所有面板排序，而常见的接受阈值会压缩臂间距离并反转一个面板排序。212个参考值中的54个经更新后改变了分数水平并消除了所有负分数，但未改变观测到的面板排序。探索性筛选还识别出9组面板比较，其中相似的积分分数掩盖了显著不同的终点或达成率。相关实现、固定输入和生成器已公开发布。
英文摘要
Anytime solvers return usable solutions before they terminate and improve them while time remains. Their progress is commonly summarized by a primal integral, a final gap, or convergence curves. Each summary leaves consequential choices open: how to score a run before its first feasible solution, whether poor incumbents are truncated, and whether the reference value is updated after the experiment or version-frozen beforehand. These choices become visible when runs produce no valid incumbent or improve a published best-known value. We study a normalized signed primal integral built from a bounded relative gap. It assigns an intrinsic worst value to an empty run, requires no acceptance threshold, and assigns negative instantaneous gaps to incumbents that beat a frozen reference. We compare the smooth difference-over-sum kernel with a signed version of Berthold's max-normalized gap and use the former as a working default. We also distinguish analysis-time from version-frozen reference policies and recommend reading the score with the raw final gap, mean convergence curve, and target-attainment curve. We evaluate these choices on a five-arm routing campaign and two model-fidelity ladders. The two signed kernels preserve every panel ordering in this study, whereas a common acceptance threshold compresses the distances between arms and reverses one panel ordering. Updating 54 of the 212 reference values changes score levels and removes all negative scores, while leaving the observed panel orderings unchanged. An exploratory screen also identifies 12 panel comparisons in which similar integral scores conceal materially different endpoints or attainment rates. The implementation, frozen inputs, and generators are openly released.
Comments40 pages, 8 figures, 10 tables. v2 rebinds the descriptive time-sliced Hexaly arm and the two ladders to the C++ binding at 10 seeds. No conclusion changes. Extended version of a manuscript prepared for journal submission. Companion reports: arXiv:2607.23116, arXiv:2608.10079. Data and code: https://doi.org/10.5281/zenodo.22095718, https://github.com/0nyr/kayros-campaign-analysis
